Rounding Error Analysis of Mixed Precision Block Householder QR Algorithms

TL;DR

This paper develops and analyzes mixed precision Householder QR algorithms, providing error bounds and numerical experiments to demonstrate their effectiveness in reducing computational costs while maintaining accuracy.

Contribution

It introduces new mixed precision QR algorithms and offers rigorous rounding error analysis supported by numerical experiments.

Findings

Mixed precision QR algorithms achieve significant speed-ups.

Error analysis confirms stability comparable to traditional methods.

Numerical experiments validate theoretical error bounds.

Abstract

Although mixed precision arithmetic has recently garnered interest for training dense neural networks, many other applications could benefit from the speed-ups and lower storage cost if applied appropriately. The growing interest in employing mixed precision computations motivates the need for rounding error analysis that properly handles behavior from mixed precision arithmetic. We develop mixed precision variants of existing Householder QR algorithms and show error analyses supported by numerical experiments.